AdvanceReview
Path to 300

Subjects / Focused study

Mathematics

5 portions covering 242 tagged questions (2020–2026). Use the interactive map below, then open a portion for full internals.

Championship framing: aim ~100 marks in Mathematics. Click donut slices to preview portions. Subject issue board →
Official · 2026

Syllabus alignment

Full unit list →

Official Math is organised as Sets/Functions, Algebra (complex, quadratic, sequences, log, P&C, binomial), Matrices, Probability & Statistics, Trigonometry, Analytical Geometry (2D+3D), Differential & Integral Calculus, and Vectors. AdvanceReview maps these into five study portions that match paper tagging.

  1. 1

    Treat Matrices + Probability as daily Algebra bank work — both are every-year.

  2. 2

    Keep Vectors & 3D fluent even at ~11% share; Paper-2 multi-correct often lives here.

  3. 3

    Practice Calculus–Conics and Complex–Trig joins; syllabus lists them separately but papers merge them.

  4. 4

    Statistics is in the official syllabus — do not skip mean/variance of a random variable.

Browse 10 unitsOfficial PDF
Visual · interactive

Understand this subject fast

Gauges for 300 + clickable topic map.

300 gauges for Mathematics

88Floor
100Target
110Stretch

Bank Algebra + Calculus early. Conics and Vectors must be attemptable every paper. Trig equations for matching/lists.

Click a portion to preview

Mathshare

Algebra

Turn Algebra into a scoring bank: matrices, probability, complex, P&C and relations appear every year.

Open internals →
Distribution

Topic weight

Cross-subject trends →
  • Algebra90 · 37.2%
  • Calculus69 · 28.5%
  • Coordinate Geometry31 · 12.8%
  • Vectors & 3D27 · 11.2%
  • Trigonometry25 · 10.3%
Drill-down

Portions

Each opens full internal coverage for focused planning.

Algebra

high

90 Q · 37.2% of subject · Core · daily · Falling share

Turn Algebra into a scoring bank: matrices, probability, complex, P&C and relations appear every year.

ProbabilityMatricesSets/RelationsComplex
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Calculus

high

69 Q · 28.5% of subject · Core · daily · Falling share

Build a pipeline: limits/continuity → derivatives/AOD → DE → definite integrals/area.

AODDefinite IntegralsContinuity/DifferentiabilityFunctions
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Coordinate Geometry

medium

31 Q · 12.8% of subject · Core · weekly · Falling share

Master conics as linked systems: parabola/ellipse/hyperbola + circle + tangent conditions.

ParabolaCircleStraight lineEllipse
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Vectors & 3D

medium

27 Q · 11.2% of subject · Core · weekly · Rising

Be fluent in planes, lines, feet of perpendiculars, and vector triple products under MC/NUM.

3D GeometryVectors
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Trigonometry

medium

25 Q · 10.3% of subject · Core · weekly · Stable

Equation solving + inverse trig principal values — often a matching/list separator.

Trigonometric EquationsInverse TrigonometryTriangle/Trigonometry
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Trend internals

Share of subject by year

Percent of this subject’s tagged questions in each year.

YearTotalAlgebraCalculusCoordinate GeometryVectors & 3DTrigonometry
202036
202138
202234
202334
202434
202532
202634

Summary

  • 5 top-level topics covering 242 tagged questions.
  • Core-daily intensity topics: Algebra, Calculus.
  • Rising topics: Vectors & 3D.
  • Falling topics: Algebra, Calculus, Coordinate Geometry.

Planning tips

  • Allocate weekly hours roughly proportional to shareOfSubject, then boost rising topics by +20%.
  • Inside each topic, drill the top 2–3 subtopics first — they usually carry >50% of that topic.
  • Use typeMix: if MC% is high, practise option-elimination; if NUM% is high, timed calculation.
  • Link weeklyPlan items to relatedMixedIds so joins are practised, not only silos.
Schedule

Study intensity map

TopicShareIntensityTrendTop subtopics
Algebra37.2% · 90 Qcore-dailyfallingProbability, Matrices, Sets/RelationsDetails →
Calculus28.5% · 69 Qcore-dailyfallingAOD, Definite Integrals, Continuity/DifferentiabilityDetails →
Coordinate Geometry12.8% · 31 Qcore-weeklyfallingParabola, Circle, Straight lineDetails →
Vectors & 3D11.2% · 27 Qcore-weeklyrising3D Geometry, VectorsDetails →
Trigonometry10.3% · 25 Qcore-weeklystableTrigonometric Equations, Inverse Trigonometry, Triangle/TrigonometryDetails →
Connections

Sample mixed joins

All mixed →
Mathematics2026 · Paper 2 · Q15–Q16linked-numerical

Exponential curves + area

Calculus – Curves+Definite Integration – Area+Trigonometric equations

Knowledge bridge

Step 1: set y = e^{-x} equal to y = e^{-x}(sin x + cos x) and cancel the common exponential to get a trig equation for intersection abscissae α_i. Step 2: order those roots and set up the definite integral of the difference of the two curves between α_1 and α_4 for the enclosed area β. Step 3: simplify the given log expression in β to a clean numerical value.

Why it feels hard

The stem hides trig solving inside an exponential envelope; students often integrate before finding exact limits.

What to practise

Drill ‘cancel common positive factor → trig roots → area integral’ as one reflex chain.

Open 2026 year review →
Mathematics2026 · Paper 2 · Q17–Q18linked-numerical

Ellipse intersection + angle + common area

Coordinate Geometry – Ellipse+Tangents & angle between curves+Area of common region

Knowledge bridge

Step 1: solve the two ellipse equations simultaneously for the first-quadrant intersection P. Step 2: differentiate implicitly to get slopes of both tangents at P; convert the angle formula into 4 tan θ. Step 3: for the common area, set up the integral (or standard ellipse-sector form) of the overlapping region and read cot α from that area.

Why it feels hard

Two different asks on one geometry figure — angle then area — under numerical fatigue.

What to practise

For two conics, always compute intersection → slopes → area in that fixed order.

Open 2026 year review →
Mathematics2026 · Paper 2 · Q8multi-correct

DE solution + extrema + intersections

Differential Equations+Functions / AOD+Curve intersections

Knowledge bridge

Step 1: solve x y' = y − x³ (homogeneous/linear in y/x) to get the family y = Cx − x³/2. Step 2: impose the given condition to fix C, then use y' = 0 to locate the local max. Step 3: compare monotonicity on (1,2) and count positive roots of f = g.

Why it feels hard

Multi-correct options test DE, calculus and graph reading together; one sign error in the DE kills several options.

What to practise

After every DE, immediately ask: extrema? monotonicity? intersections with a given g?

Open 2026 year review →